You have to give writer-director George Nolfi credit for being bold: He’s used a Philip K. Dick short story as the springboard for a movie with the soul of a 1940s romantic fantasy and the trappings of a 1970s paranoia picture. A peculiar combination, but “The Adjustment Bureau” plays out much more smoothly than it should, considering it’s something of a sheep in wolf’s clothing — a thoughtful, almost whimsical caper in which menace and danger linger in the background and lurk around on the sidelines without ever really taking center stage.

It’s rather gutsy of Nolfi to defy convention and confound expectations in what’s being packaged as a slick, tense chase movie with ominous science-fiction overtones.

Based very loosely on Dick’s 1954 tale “The Adjustment Team,” the movie has some fun dropping evocative images of Eisenhower-era America into the all-electronic society of cell phones, text messaging and “The Daily Show.” The members of the vaguely defined Adjustment Bureau dress like extras from “The Man in the Gray Flannel Suit” or “Revolutionary Road,” complete with fedoras. A few years ago, they might have stood out as retro relics in Manhattan; these days, they look like they’re on their way to a “Mad Men” marathon (in fact, one of the leaders, referred to only as Richardson, is played by “Mad Men” vet John Slattery).

When they talk about reporting to the all-powerful Chairman, you might half-expect Frank Sinatra to show up.

The Bureau’s mission is to preserve The Plan, which is laid out in notebooks that open up to reveal constantly shifting grids and pulsating, roving dots reminiscent of the Marauders’ Map in the Harry Potter chronicles. This seems to be serious, often strenuous work, requiring split-second timing and, occasionally, a bit of tampering with the elements. If a New Yorker isn’t supposed to reach his destination, the Bureau boys use their powers to make sure every cab in the city whizzes right by him; if a power-player is about to make a decision that could negatively affect The Plan, the team drops by his office, puts everyone into suspended animation for a few minutes and performs a little brainwashing on the potential problem child.

It sounds dark and devious, but Nolfi treats it as casually as if the Adjustment Bureau was dropping in to do a meter reading or perform a few software upgrades. To be honest, the micromanaging staffers don’t seem much more threatening than Clarence the apprentice guardian angel in “It’s a Wonderful Life,” or the suave, otherworldly administrator Mr. Jordan (Claude Rains) from “Here Comes Mr. Jordan” and “Down to Earth.”

Think of them as well-groomed gremlins adhering to a strict agenda.

“Sometimes people spill their coffee, or their Internet goes out, or they misplace their keys, and they think it’s chance,” Richardson explains to bewildered politician David Norris (Matt Damon). “Sometimes it is; sometimes it’s us.”

David, an aspiring Senator whose career was derailed by a dredged-up scandal, runs afoul of the Bureau after a chance encounter with Elise Sellas (Emily Blunt), a rising star in the world of modern dance. Although there’s an immediate attraction between them, there’s also a major obstacle: According to the Bureau, their romance does not compute.

“Whatever happened to free will?” David barks at the no-nonsense Thompson (Terence Stamp), who steps in to squelch the affair before it goes too far. “You don’t have free will,” Richardson replies. “You have the appearance of free will.”

“Love is a Many-Splendored Thing” was a popular theme in the time when Dick’s story first hit the newsstands, but in “Bureau,” love is more like a hassle and a half. While Elise and David seem like a perfect pair, Richardson warns of dire consequences if they follow their hearts instead of The Plan. The fascinating/frustrating choice the movie hands David is not the usual life-or-death dilemma; instead, he has to decide if he would turn his back on not only his bright future but Elise’s as well, in the name of passion.

The conflict might be easier to resolve if Damon and Blunt didn’t have knock-your-socks-off chemistry. His shy/sly looks and understated humor are wonderfully offset by her teasing nonchalance and frisky spirit. It’s a match-up on a par with Kate Winslet and Leonardo DiCaprio, or Julia Roberts and Richard Gere; there’s an intoxicating combination of electricity and effervescence in their scenes together. If there are any producers out there who want to concoct a truly irresistible romantic comedy, hiring Blunt and Damon would be a sensational start.

Nolfi utilizes them superbly, which gives his seriocomic screenplay some genuine emotional weight. The story is noteworthy because there aren’t any standard-issue evildoers out to torment David and Elise, just a bunch of duty-minded foot soldiers, like Richardson and the somewhat sympathetic Mitchell (Anthony Mackie), who are trying to do their jobs. Even though Nolfi builds the suspense as if this was a conspiracy thriller, there is very little violence or terror along the way.

Clever and fairly imaginative — if you’re willing to buy into its oddball analogy between heaven and an old-school corporation — “The Adjustment Bureau” is entertaining enough to be worthwhile. Even so, it’s the magnetism of its two enormously appealing stars that makes an above-average movie into something special.